Multi-span Suspension Bridges Research Articles

Large deformation assessment of three-tower suspension bridges: An enhanced analytical model and solution algorithm

An enhanced nonlinear approach is proposed in this study to address the limitations of traditional deflection theory in analyzing large deformations of three-tower suspension bridges. In this approach, the three-tower suspension bridge is simplified as two quasi-independent bridges for analysis, and detailed considerations are given to the vertical and longitudinal deformations of the main cable, which produce the expression for the relationship between the cable's internal force and deformations. By employing the complementary energy principle and variational calculus, the nonlinear differential equations describing bridge deformations are then established. To ensure the displacement continuity at the middle tower, this paper proposes the use of Chebyshev polynomials to approximate the solutions of the differential equations, and the weighted residual method is then used to transform these differential equations into algebraic equations. On this basis, the developed nonlinear adjustment optimization algorithm enables efficient solving of the nonlinear equation and thus determination of bridge deformation under various load conditions. The accuracy and effectiveness of the proposed scheme are validated through the analysis of two suspension bridges with equal and unequal spans. Finally, the extended applications of the proposed scheme on the other type of multi-span suspension bridges are introduced for further applications.

Nonlinear static solution of suspension bridge formulated from a surrogate model with secant stiffness of suspension cables

Explicit analytical solution may offer great convenience for the design and parametric study of suspension bridges. However, the nonlinear behavior of suspension cable exacerbates the difficulty of such theoretical derivation. Adopting secant stiffness is an effective way to deal with the nonlinearity of the cable, but the crux is how to find its deformed state under external loading. The strategy of this study is primarily targeted at a typically arranged three-span suspension bridge. It starts from formulating the basic form of nonlinear stiffness of suspension cables by setting the elastic stiffness and geometric stiffness in series, then a surrogate model is accordingly established with the nonlinear springs to replace the mid-span and side-span cables. The deformed state of the surrogate model subjected to the specified external load cases will be found by restricting and releasing its tower tops, and thus the analytical formula of the secant stiffness can be obtained. Consequently, the nonlinear static solution of suspension bridge, including force and deformation changes in the cables and towers, can be explicitly expressed with the secant stiffness. The general solution procedure can also be extended to multi-span suspension bridges. Finally, the nonlinear static solution is verified by numerical examples of a three-span suspension bridge and a four-span suspension bridge. The parametric analysis reveals that the nonlinearity of suspension bridge will become significant as the side-span to mid-span ratio increases, or when the side-span cables are hung with hangers.

Dynamic response of a multi-span suspension bridge subjected to highway vehicle loading

Dynamic response of a multi-span suspension bridge subjected to highway vehicle loading

Static response of a multi-span suspension bridge subjected to highway vehicle loading

Static response of a multi-span suspension bridge subjected to highway vehicle loading

Competing mechanism between vertical stiffness and anti-slip safety in double-cable multi-span suspension bridges

Double-cable multi-span suspension bridges (double-cable bridges) have great development prospects in long-span bridge engineering. The vertical stiffness of the bridge and the anti-slip safety between the cable and saddle are the two primary competing factors governing the preliminary design of double-cable bridges. It is essential to study the competing mechanism between these two factors to determine reasonable parameters for designing sustainable double-cable bridges. In this study, the deflection-span ratio and anti-slip safety coefficient were adopted as indices to evaluate the vertical stiffness and anti-slip safety, respectively. Finite-element analysis was performed to investigate the influence of the main design parameters on the relationship between the deflection-span ratio and anti-slip safety coefficient and to clarify the competing mechanism between these two factors. Finally, we propose some recommendations for the preliminary design of double-cable bridges. The results of our study reveal that increasing the bending stiffness of the middle tower, increasing the constant load distribution ratio, or installing vertical friction plates in the top sub-saddle are useful in expanding the application scope of double-cable bridges. This study provides new insights into the competing mechanism between the vertical stiffness and anti-slip safety of double-cable bridges.

Analytical formulation of the temperature‐induced deformation of multispan suspension bridges

Analytical formulation of the temperature‐induced deformation of multispan suspension bridges

Fatigue failure of welded details in steel bridge pylons

Multi-span suspension bridges show special structural characteristics compared with conventional suspension bridges. The mid-pylon is vulnerable to fatigue failure due to the effects of wind loads and traffic loads. In this study, based on the engineering context of the Taizhou Yangtze River Bridge, some investigations were conducted on the structural behaviour of this multi-span suspension bridge. Fatigue strength tests of two critical details on the steel mid-pylon were carried out. The two details were the butt weld of two segments near the longitudinal full penetration weld and the longitudinal full penetration weld near the diaphragm. Crack propagation was observed in the tests, and it was found that the initial crack propagation directions of the two details were different. S-N curves for these two details are not included in relevant bridge design codes, and in this study, fatigue strength values of the two details are proposed based on their fatigue tests. It is suggested that the fatigue strength value corresponding to two million-cycles for the detail of the butt weld of two segments near the longitudinal full penetration weld is 85.6 MPa, and the fatigue strength value corresponding to two million-cycle for the detail of the longitudinal full penetration weld near the diaphragm is 101.5 MPa.

Frictional Resistance between Main Cable and Saddle for Suspension Bridges. I: Friction Characteristic of Single Strand

Abstract The frictional resistance between main cable and saddle of a long-span, multispan suspension bridge is significant for the safety of the bridge. Typically, the main cable of a long-span, m...

Antislip Safety of Double-Cable Multispan Suspension Bridges with Innovative Saddles

Abstract Compared with suspension bridges with a single main cable in each cable plane, adding a cable with a different sag may increase the vertical stiffness, but also increase the demand of fric...

中央径間長 3000m を有する超長大多径間吊橋の耐風安定性に関する基礎的検討

中央径間長 3000m を有する超長大多径間吊橋の耐風安定性に関する基礎的検討

Wind stability of twin box girder multi-span suspension bridges with 3000-meter center of span length

Wind stability of twin box girder multi-span suspension bridges with 3000-meter center of span length

Aerostatic instability mode analysis of three-tower suspension bridges via strain energy and dynamic characteristics

Multispan suspension bridges make a good alternative to single-span ones if the crossed strait or river width exceeds 2-3 km. However, multispan three-tower suspension bridges are found to be very sensitive to the wind load due to the lack of effective longitudinal constraint at their central tower. Moreover, at certain critical wind speed values, the aerostatic instability with sharply deteriorating dynamic characteristics may occur with catastrophic consequences. An attempt of an in-depth study on the aerostatic stability mode and damage mechanism of three-tower suspension bridges is made in this paper based on the assessment of strain energy and dynamic characteristics of three particular three-tower suspension bridges in China under different wind speeds and their further integration into the aerostatic stability analysis. The results obtained on the three bridges under study strongly suggest that their aerostatic instability mode is controlled by the coupled action of the anti-symmetric torsion and vertical bending of the two main-spans\' deck, together with the longitudinal bending of the towers, which can be regarded as the first-order torsion vibration mode coupled with the first-order vertical bending vibration mode. The growth rates of the torsional and vertical bending strain energy of the deck after the aerostatic instability are higher than those of the lateral bending. The bending and torsion frequencies decrease rapidly when the wind speed approaches the critical value, while the frequencies of the anti-symmetric vibration modes drop more sharply than those of the symmetric ones. The obtained dependences between the critical wind speed, strain energy, and dynamic characteristics of the bridge components under the aerostatic instability modes are considered instrumental in strength and integrity calculation of three-tower suspension bridges.

Numerical study on cable-saddle frictional resistance of multispan suspension bridges

For multispan suspension bridges, the frictional resistance between main cable and saddle is vital to counterpoise unbalanced cable tension between adjacent main spans. The calculation for frictional resistance is essential for the bridge design. In this study, a numerical method for frictional resistance between main cable and saddle is developed. The proposed method is validated against large-scale saddle model tests, and then used to analyze the frictional resistance in a multispan suspension bridge. The method is used to investigate the main components of total frictional resistance, the effects of vertical friction plates, and the frictional resistance distribution along the longitudinal direction of saddle. The results indicate that the frictional resistance at the bottom and side surfaces between main cable and saddle are the main components of total frictional resistance. The distribution of frictional resistance along the longitudinal direction of saddle increases from one end to the other end of saddle. To add vertical friction plates is an effective way to increase the frictional resistance. The proposed numerical method provides an effective and feasible tool for evaluating the frictional resistance.

Coupled aerodynamic and hydrodynamic response of a long span bridge suspended from floating towers

The present study introduces a fully coupled time-domain analysis of a multi-span suspension bridge supported by two floating towers, considered for crossing the wide and deep fjords along the west coast of Norway. The time-domain analysis is performed with a finite element model considering simultaneously the turbulent wind, irregular inhomogeneous ocean waves and sheared ocean current. The numerical results suggest that under extreme conditions with a return period of 100 years, the bridge horizontal response is dominant and governed by the low-frequency modes. For the vertical and torsional responses, the largest contributions are due to the respective motion components of the low-frequency horizontal motion-dominated modes. The investigation into the significance of the aerodynamic and hydrodynamic load reveals that in the case studied, over 80% of the bridge girder response is due to the aerodynamic excitation. The hydrodynamic loads acting on the floating towers are small due to a relatively small significant wave height in the fjord and the counteracting aerodynamic damping effect. By considering the inhomogeneity of the waves, i.e. different conditions at the two floating supports, the contribution of the aerodynamic action to the lateral, vertical and torsional dynamic responses increases by 6%, 7% and 9% respectively.

Load carrying capacity of super long multi-span suspension bridges with various number of spans and sag ratio

Load carrying capacity of super long multi-span suspension bridges with various number of spans and sag ratio

Minimum geotechnical requirements for traditional and singular bridges foundations design: Chacao Suspension Bridge

Bridges projects, usually considered a wide range of geotechnical research for the design of foundations. These works are of considerable importance for the proper design of foundations (shallow or deep) as well as to avoid problems during the project execution (time, cost, safety, complementary campaigns, etc.). This paper aims to analyze criteria and minimum geotechnical requirements for the project development of traditional and long-span bridges in Chile, taking into account international and national experience, considering as case of study the Project of Design and Construction of Chacao Bridge: multi-span suspension bridge with two main spans, 1,055 m and 1,155 m, currently underway in southern Chile, as a result of this work a summary of the minimum geotechnical requirements needed is proposed.

Analytical Models of Frictional Resistance between Cable and Saddle Equipped with Friction Plates for Multispan Suspension Bridges

Analytical Models of Frictional Resistance between Cable and Saddle Equipped with Friction Plates for Multispan Suspension Bridges

16.01: Bjørnafjorden suspension bridge TLP concept

ABSTRACTThe Bjørnafjorden TLP (Tension Leg Platform), a multi span suspension bridge solution, is one of the possible fjord crossings options considered as part of the ambitious “Ferry‐free Coastal Highway E39” under development in Norway. The original design concept for Bjørnefjorden was very much similar to that of a conventional suspension bridge using central locks between main cable and bridge deck to distribute movements equally to the bridge ends. However since the bridge is of the multi‐span type, the inherent flexibility of the pylons caused a severe of in‐plane stability of the original system leading to large vertical displacement of the deck. To mitigate this effect top cables have been introduced between pylon tops preventing these from excessive longitudinal displacements and thereby also limiting the vertical deck displacement from traffic load. In this paper the different concept challenges for the Bjørnafjorden TLP solution is outlined.The suspension bridge has a total of four pylons – a northern and southern pylon of concrete located near shore, while two central steel pylons are supported by TLP's at 550m and 450m depth. The TLP's, as well known from off‐shore industry, consist of pre‐tensioned steel pipes anchored in the seabed and at the surface connected to a large steel “floaters” onto which the towers are placed. The main spans are 1300–1400m and the bridge has an overall length from anchorage to anchorage of about 5200m.Due to the long tethers of the TLP the central pylons are relatively unrestrained to move up to 20m horizontally and thus in order to achieve sufficient stability of the bridge system a special feature in form of top cables are introduced. The top cables connect the tower top of all four pylons and are anchored to the bridge anchor blocks together with the main cable.The bridge structural system is the outcome of innovative thinking and a fine example on how a few unconventional features can make a very conventional bridge system work in challenging conditions. As the bridge is floating it is essential that the structure is light and therefore the primary structures are in steel.

Sliding Resistance of Main Cables in Double-Cable Multispan Suspension Bridges

Sliding Resistance of Main Cables in Double-Cable Multispan Suspension Bridges

Multiple-span suspension bridges: state of the art

This paper provides a state-of-the-art review of the design and construction of multiple-span suspension bridges. It starts with a brief introduction to the key issues associated with multi-span suspension bridges and then gives a historical review of this bridge form together with a list of multi-span suspension bridges constructed from 1800 to the present day. The paper looks at and compares the deflection characteristics of the classic suspension bridge with multi-span suspension bridges. The paper outlines the problems associated with this bridge form, primarily caused by increased flexibility, and the ways that they can be and have been overcome. Actual bridges where they exist (or formerly existed) are referred to and the paper also looks at some current and proposed future projects using multiple-span suspension bridges. Much of the recent work on this subject has been carried out in China, and translations of the abstracts of some recent Chinese papers are included in an appendix to the paper.